Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian.

Journal Article (Journal Article)

The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a non-trivial task of practical importance. In image analysis this manifests for example in anomaly detection and target detection. The traditional spectral clustering algorithm, which relies on the leading K eigenvectors to detect K clusters, fails in such cases. In this paper we propose the spectral embedding norm which sums the squared values of the first I normalized eigenvectors, where I can be significantly larger than K . We prove that this quantity can be used to separate clusters from the background in unbalanced settings, including extreme cases such as outlier detection. The performance of the algorithm is not sensitive to the choice of I , and we demonstrate its application on synthetic and real-world remote sensing and neuroimaging datasets.

Full Text

Duke Authors

Cited Authors

  • Cheng, X; Mishne, G

Published Date

  • January 2020

Published In

Volume / Issue

  • 13 / 2

Start / End Page

  • 1015 - 1048

PubMed ID

  • 34136062

Pubmed Central ID

  • PMC8204716

Electronic International Standard Serial Number (EISSN)

  • 1936-4954

International Standard Serial Number (ISSN)

  • 1936-4954

Digital Object Identifier (DOI)

  • 10.1137/18m1283160

Language

  • eng